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A body of density d and volume V floats with volume $V_1$ of it immersed in a liquid of density $d_1$ and rest of the volume $V_2$ immersed in another liquid of density $d_2$(<$d_1$) then $V_1$ is

Energy is being emitted from the surface of a black body at ${127}^{o}C$ temperature at the rate of $1.0\times {10}^{6}J/sec-m^2$. Temperature of the black body at which the rate of energy emission is $16.0\times {10}^{6}J/sec-m^2$ will be

An $U-$ tube of base length ${}^{\prime }{l}^{\prime }$ filled with the same volume of two liquids of densities $\rho$ and $2\rho$ is moving with an acceleration ${}^{\prime }{a}^{\prime }$ on the horizontal plane, as shown in the figure. If the difference in heights of the liquid columns in the two vertical limbs (open to the atmosphere) is zero, then the height $h$ is given by

A loaded vertical spring executes simple harmonic oscillations with period of 4 s. The difference between the kinetic energy and potential energy of this system oscillates with a period of

Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

Let $I={\int }_0^1\frac{e^x}{1+x}dx$
${\int }_0^1\frac{x^2{e}^x}{x+1}dx$ equals

A ball of mass $m$ moving with speed $u$ undergoes a head on perfect elastic collision with mass $nm$ initially at rest. The fraction of the energy transferred to the second ball by the first ball is

Figure shows a loop-the-loop track of radius R. A car (without engine) starts from a platform at a distance h above the top of the loop and goes around the loop without falling off the track. Find the minimum value of h for a successful looping. Neglect friction

A cell can be balanced against 140 cm and 120 cm of uniform potentiometer wire, with and without being short circuited through a resistance of $7\Omega$ respectively. Find the internal resistance of the cell

A wire of resistance 5 ohm is drawn out so that its new length is three times its original length. What is the resistance of the new wire ?

A uniform wheel of radius R is set into rotation about its axis at an angular speed $\omega$. This rotating wheel is now placed on a rough horizontal surface with its axis horizontal. Because of friction at the contact, the wheel accelerates forward and its rotation decelerates till the wheel starts pure rolling on the surface. Find the linear speed of the wheel after it starts pure rolling.

A block of mass M is placed on the top of a bigger block of mass 10 M as shown in figure.All the surfaces are frictionless. The system is released from rest. Find the distance moved by the bigger block at the instant the smaller block reaches the fround.

The geostationary orbit of the earth is at a distance of about 36000 km from the earth's surface. Find the weight of a 120-kg equipment placed in a geostationary satellite. The radius of the earth is 6400 km.

There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

What is zener diode . How can a zener diode be used as a voltage regulator. Explain using suitable circuit diagram.

A block of mass 1 kg is left on a smooth incline that ends into a circular track of radius 1m. Find the work done by gravity on the block till the point reaches the top most point of the circular track.

The wave function $\left(\Psi \right)$ of $2s$ is given by:
${\Psi }_{2s}=\frac{1}{2\sqrt{2\pi }}{\left(\frac{1}{a_0}\right)}^{\frac{1}{2}}\{2-\frac{r}{a_0}\}{e}^{-r/2a_0}$
At $r=r_0$ radial node is formed. Thus for $2s$, $r_0$ in terms of $a_0$ is:

A cinema hall has equidistant rows 1 m apart. The length of the cinema hall is 287 m and it has 287 rows. From one side of the cinema hall, laughing gas(N₂O) is released and from the other side, tear gas(C₆H₅COCH₂CI) is released. In which rows, spectators will be laughing and weeping simultaneously?

A conducting circular loop of radius r carries a constant current i. It is placed in a uniform magnetic field B such that B is perpendicular to the plane of the loop. The magnetic force acting on the loop is

Electric field at the surface of a charged conductor is proportional to

In the figure shown, find the direction of friction on blocks B and C at the surface which is common to the blocks B and C respectively.

The period of oscillation of a magnet of momentum p_m is 1.5s. If we use a bar magnet of same moment of inertia but moment 9p_m, the time period of oscillation will be:

If velocity is given as $v=\alpha -\beta x$, then dimensional formula of $\beta {\alpha }^2$ is

Find the acceleration of block of mass ${}^{\prime }4m^{\prime }$, assuming that the surface and pulley are smooth and the string is inextensible.

In an elastic collision of two particles the following is conserved

Figure shows three containers. The rightmost container contains water (heat capacity $5cal{/}^{\circ }C$), initially at temperature ${100}^{\circ }\text{C}$. The middle container contains water maintained at ${80}^{\circ }\text{C}$ with the help of a heater. The container at the left hand side contains ice at $0^{\circ }\text{C}$. There are two heat conducting rods $A$ and $B$ both having thermal resistance equal to ${10}^{\circ }\text{C}\text{s/cal}$. Disregard any heat loss in the surrounding.


Initially, what is the power of heater required to maintain the temperature of middle container at ${80}^{\circ }\text{C}$?

If in a medium wave's wavelength is decreased, what will happen to its frequency?

If a body is rotating about a given Axis and a Force is applied at any point on that body along any random direction, what can we say about the torque of this force about any point lying on its Axis of rotation?

When a point source of light is at a distance of one metre from a photo cell, the cut off voltage is found to be V. If the same source is placed at 2 m distance from photo cell, the cut off voltage will be

In a series RCL circuit at resonance the applied ac voltage is 220 V. The potential drop across the inductance is 110V, what is the potential drop across the capacitor?

Given that $0.2\hat{i}+0.6\hat{j}+a\hat{k}$ is a unit vector. What is the value of a?

The momentum of the photon of wavelength $5000\dot{A}$ will be

A 250-turn rectangular coil of length $2.1cm$ and width $1.25cm$ carries a current of 85 $\mu A$ and subjected to a magnetic field of strength $0.85T$. Work done in rotating the coil by ${180}^0$ against the torque is

A stone is placed at the bottom of lake of depth $10m$. Refractive index of water of lake is $\mu =(1+\frac{y}{10})$ where $y$ is depth of water from surface. A person looks at stone normally, then depth at which stone appears to him in meters is ($ln2=0.693$)

For a diode connected in parallel with a resistor, which is the most likely current(I)-voltage(V) characteristic?

A body floats in a liquid contained in a beaker. If the whole system as shown in figure falls freely under gravity, then the upthrust on the body due to liquid is

A small air bubble is trapped inside a transparent cube of side 12 cm. When viewed from one of the vertical faces, the bubble appears to be at 5 cm from it. When viewed from opposite face, it appears at 3 cm from it.

In the equation $\int \frac{dv}{v^{\frac{3}{2}}}=BC{e}^{-2Ct}$, where $v$ is velocity, $t$ is time, $e$ is Euler's number. The dimensions of $B$ are

A ball is thrown vertically downwards from a height of 20m with an initial velocity $v_0$. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity $v_0$ is:

A block of mass m is attached with massless spring of force constant k. The block is placed over a fixed rough
inclined surface for which the coefficient of friction is $\mu =\frac{3}{4}.$The block of mass m is initially at rest. The block
of mass M is released from rest with spring in unstretched state. The minimum value of M required to move the
block up the plane is (neglect mass of string and pulley and friction in pulley.)

The time taken by the projectile to reach from A to B is t. Then the distance AB is equal to

A rod AB of length L is hung from two identical wires 1 and 2. A block of mass m is hung at point O of the rod as shown in fig. The value of x so that a tuning fork excites the fundamental mode in wire 1 and the second harmonic in wire 2 is